This project report is concerned with a real-life distribution problem. The 
objective is to optimize a distribution of work-shifts between separate 
departments. The problem is approached algorithmically. 

How well we are able to model a problem in an algorithm and how
fast this algorithm runs are the basic means of measuring the quality of an
algorithm. However, some problems are too hard to be solved optimally within a
reasonable time. It is therefore appropriate to approximate the solution, by
accepting an in general good solution in favor of a naive one.

This project report is concerned with such a problem. The real-life application
is to distribute phone-shifts over call centers that are located in different
parts of the country. The distribution is bound to some constraints, for example
that the distribution amongst departments must be equal over a quarter and over
each week.

When facing this problem, a number of possibilities arise on how to solve
it. While approaches towards finding optimal solutions are clearly existing,
their feasibility can be questionable.

The focus of this project report is to develop a local search algorithm that
approximates the optimal solution. We will, over the course of the report,
analyze this approach and compare it to a brute force search, which
theoretically always yields the correct result.

The remainder of this report is structured as follows: Next, we will introduce
the problem in more detail, formalizing it where necessary. In section three, we
will outline a number of different approaches, including variants of local
search, supplied with pseudo-code to make our reasoning more graspable. This
section is followed by a run-time analysis of relevant parts of our algorithm,
as well as an analysis of the brute force approach. Finally, we will briefly
discuss the quality of our solution and the result our algorithm produces and
then conclude with an overview over what we learn over the course of this
project and an outline of possible enhancements to our approach.
